The number
A068934(n,r) of connected r-regular (simple) graphs on n vertices.
Girth at least:
3
4
5
6
7
8
| A005177
|
  |
  |
  |
  |
A002851 |
A006820 |
A006821 |
A006822 |
A014377 |
A014378 |
A014381 |
A014382 |
A014384 |
| all r |
n\r |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
| 1 |
1 |
1 |
| 1 |
2 |
0 |
1 |
| 1 |
3 |
0 |
0 |
1 |
| 2 |
4 |
0 |
0 |
1 |
1 |
| 2 |
5 |
0 |
0 |
1 |
0 |
1 |
| 5 |
6 |
0 |
0 |
1 |
2 |
1 |
1 |
| 4 |
7 |
0 |
0 |
1 |
0 |
2 |
0 |
1 |
| 17 |
8 |
0 |
0 |
1 |
5 |
6 |
3 |
1 |
1 |
| 22 |
9 |
0 |
0 |
1 |
0 |
16 |
0 |
4 |
0 |
1 |
| 167 |
10 |
0 |
0 |
1 |
19 |
59 |
60 |
21 |
5 |
1 |
1 |
| 539 |
11 |
0 |
0 |
1 |
0 |
265 |
0 |
266 |
0 |
6 |
0 |
1 |
| 18979 |
12 |
0 |
0 |
1 |
85 |
1544 |
7848 |
7849 |
1547 |
94 |
9 |
1 |
1 |
| 389436 |
13 |
0 |
0 |
1 |
0 |
10778 |
0 |
367860 |
0 |
10786 |
0 |
10 |
0 |
1 |
| 50314796 |
14 |
0 |
0 |
1 |
509 |
88168 |
3459383 |
21609300 |
21609301 |
3459386 |
88193 |
540 |
13 |
1 |
1 |
| 2942198440 |
15 |
0 |
0 |
1 |
0 |
805491 |
0 |
1470293675 |
0 |
1470293676 |
0 |
805579 |
0 |
17 |
0 |
1 |
| 1698517036411 |
16 |
0 |
0 |
1 |
4060 |
8037418 |
2585136675 |
113314233808 |
733351105934 |
733351105935 |
113314233813 |
2585136741 |
8037796 |
4207 |
21 |
1 |
1 |
|   |
17 |
0 |
0 |
1 |
0 |
86221634 |
0 |
9799685588936 |
0 |
  |
0 |
9799685588961 |
0 |
86223660 |
0 |
25 |
0 |
1 |
|   |
18 |
0 |
0 |
1 |
41301 |
985870522 |
2807105250897 |
  |
  |
  |
  |
  |
  |
2807105258926 |
985883873 |
42110 |
33 |
1 |
1 |
|   |
19 |
0 |
0 |
1 |
0 |
11946487647 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
11946592242 |
0 |
39 |
0 |
1 |
|   |
20 |
0 |
0 |
1 |
510489 |
152808063181 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
152808993767 |
516344 |
49 |
1 |
1 |
|   |
21 |
0 |
0 |
1 |
0 |
2056692014474 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
2056701139136 |
0 |
60 |
0 |
1 |
|   |
22 |
0 |
0 |
1 |
7319447 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
7373924 |
73 |
1 |
1 |
|   |
23 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
88 |
0 |
1 |
|   |
24 |
0 |
0 |
1 |
117940535 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
118573592 |
110 |
1 |
1 |
|   |
25 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
130 |
0 |
1 |
|   |
26 |
0 |
0 |
1 |
2094480864 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
2103205738 |
158 |
1 |
1 |
|   |
27 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
191 |
0 |
1 |
|   |
28 |
0 |
0 |
1 |
40497138011 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
40634185402 |
230 |
1 |
1 |
|   |
29 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
273 |
0 |
1 |
|   |
30 |
0 |
0 |
1 |
845480228069 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
847871397424 |
331 |
1 |
1 |
|   |
31 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
391 |
0 |
1 |
|   |
32 |
0 |
0 |
1 |
18941522184590 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
18987149095005 |
468 |
1 |
1 |
|   |
33 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
556 |
0 |
1 |
|   |
34 |
0 |
0 |
1 |
453090162062723 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
454032821688754 |
660 |
1 |
1 |
|   |
35 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
779 |
0 |
1 |
|   |
36 |
0 |
0 |
1 |
11523392072541432 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
11544329612485981 |
927 |
1 |
1 |
|   |
37 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
1087 |
0 |
1 |
|   |
38 |
0 |
0 |
1 |
310467244165539782 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
310964453836198311 |
1284 |
1 |
1 |
|   |
39 |
0 |
0 |
1 |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
  |
0 |
1510 |
0 |
1 |
|   |
40 |
0 |
0 |
1 |
8832736318937756165 |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
  |
8845303172513781271 |
1775 |
1 |
1 |